| Title: | Rigidity of terminal simplices in persistent homology |
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| Authors: | ID Franc, Aleksandra (Author)
ID Virk, Žiga (Author) |
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| Files: |  URL - Source URL, visit https://link.springer.com/article/10.1007/s13398-023-01473-z
 PDF - Presentation file, download (476,36 KB)
MD5: BA951B107E513AAEE2E68383B2703D7D
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| Language: | English |
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| Typology: | 1.01 - Original Scientific Article |
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| Organization: |  IMFM - Institute of Mathematics, Physics, and Mechanics
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| Abstract: | Given a filtration function on a finite simplicial complex, stability theorem of persistent homology states that the corresponding barcode is continuous with respect to changes in the filtration function. However, due to the discrete setting of simplicial complexes, the simplices terminating matched bars cannot change continuously for arbitrary perturbations of filtration functions. In this paper we provide a sufficient condition for rigidity of a terminal simplex, i.e., a condition on $\varepsilon > 0$ implying that the terminal simplex of a homology class or a bar in persistent homology remains constant through $\varepsilon$-perturbations of filtration function. The condition for a homology class or a bar in dimension $n$ depends only on the barcodes in dimensions $n$ and $n+1$. |
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| Keywords: | persistent homology, stability theorem, terminal simplex, rigidity |
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| Publication status: | Published |
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| Publication version: | Version of Record |
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| Publication date: | 01.10.2023 |
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| Year of publishing: | 2023 |
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| Number of pages: | str. 1-16 |
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| Numbering: | Vol. 117, iss. 4, article no. 141 |
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| PID: | 20.500.12556/DiRROS-18417  |
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| UDC: | 515.1 |
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| ISSN on article: | 1578-7303 |
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| DOI: | 10.1007/s13398-023-01473-z |
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| COBISS.SI-ID: | 157780483 |
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| Publication date in DiRROS: | 15.03.2024 |
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| Views: | 469 |
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| Downloads: | 227 |
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